Question 168
Solve the following system of equations:
$$
\begin{cases}
\frac{1}{\sqrt{1+2x^2}} + \frac{1}{\sqrt{1+2y^2}} = \frac{2}{\sqrt{1+2xy}} \\
\sqrt{x(1-2x)} + \sqrt{y(1-2y)} = \frac{2}{9}
\end{cases}
$$
$$
\begin{cases}
\frac{1}{\sqrt{1+2x^2}} + \frac{1}{\sqrt{1+2y^2}} = \frac{2}{\sqrt{1+2xy}} \\
\sqrt{x(1-2x)} + \sqrt{y(1-2y)} = \frac{2}{9}
\end{cases}
$$